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We analyze mixed multi-qubit states composed of a W class state and a productstate with all qubit in |0>. We find the optimal pure state decomposition andconvex roofs for higher-tangle with bipartite partition between one qubit andthe rest qubits for those mixed states. The optimality of the decomposition isensured by the Coffman-Kundu-Wootters (CKW) inequality which describes themonogamy of quantum entanglement. The generalized monogamy inequality is foundto be true for W class states with arbitrary partitions between one qubit andmulti-qubit.

Entangled multi-qubit states without higher-tangle